A correlated series of experimental and theoretical studies regarding hormone receptor interactions has been undertaken. A variety of model systems have been utilized, including the receptors for aldosterone, corticosterone glucocorticoids, encephalins, endorphins and opiates, benzodiazepines, LHRH, insulin and beta-adrenergic agonists and antagonists. By development of appropriate mathematical models, computer programs for curve-fitting and data analysis, and of improved experimental designs, we have been able to characterize several of these ligand-receptor systems. Special attention has been given to the cases of 1) multiple ligands reacting simultaneously with multiple classes of sites; 2) the presence of multiple sub-sites on receptor areas; 3) the interaction of ligand-binding with an ionophore; 4) the interaction of receptors for different ligands on the same cell membrane; 5) the interaction of divalent ligands with the cell surface membrane.